Information on Result #684367
Linear OA(527, 36, F5, 18) (dual of [36, 9, 19]-code), using construction XX applied to C1 = C([0,47]), C2 = C([1,71]), C3 = C1 + C2 = C([1,47]), and C∩ = C1 ∩ C2 = C([0,71]) based on
- linear OA(516, 24, F5, 12) (dual of [24, 8, 13]-code), using contraction [i] based on linear OA(588, 96, F5, 51) (dual of [96, 8, 52]-code), using the expurgated narrow-sense BCH-code C(I) with length 96 | 58−1, defining interval I = [0,47], and minimum distance d ≥ |{−3,−2,…,47}|+1 = 52 (BCH-bound) [i]
- linear OA(520, 24, F5, 17) (dual of [24, 4, 18]-code), using contraction [i] based on linear OA(592, 96, F5, 71) (dual of [96, 4, 72]-code), using the narrow-sense BCH-code C(I) with length 96 | 58−1, defining interval I = [1,71], and designed minimum distance d ≥ |I|+1 = 72 [i]
- linear OA(521, 24, F5, 18) (dual of [24, 3, 19]-code), using contraction [i] based on linear OA(593, 96, F5, 75) (dual of [96, 3, 76]-code), using the expurgated narrow-sense BCH-code C(I) with length 96 | 58−1, defining interval I = [0,71], and minimum distance d ≥ |{−3,−2,…,71}|+1 = 76 (BCH-bound) [i]
- linear OA(515, 24, F5, 11) (dual of [24, 9, 12]-code), using contraction [i] based on linear OA(587, 96, F5, 47) (dual of [96, 9, 48]-code), using the narrow-sense BCH-code C(I) with length 96 | 58−1, defining interval I = [1,47], and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- linear OA(56, 11, F5, 5) (dual of [11, 5, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(56, 12, F5, 5) (dual of [12, 6, 6]-code), using
- extended quadratic residue code Qe(12,5) [i]
- discarding factors / shortening the dual code based on linear OA(56, 12, F5, 5) (dual of [12, 6, 6]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(527, 18, F5, 2, 18) (dual of [(18, 2), 9, 19]-NRT-code) | [i] | OOA Folding | |